A Hitchhiker's Guide to Endomorphisms and Automorphisms of Cuntz Algebras

Autor: Valeriano Aiello, Roberto Conti, Stefano Rossi

Publikováno v: Rendiconti di Matematica e delle Sue Applicazioni, Vol 42, Iss 1-2, Pp 61-162 (2021)

We present a broad selection of results on endomorphisms and automorphisms of the Cuntz algebras On that have been obtained in the last decades. A wide variety of open problems is also included.

Externí odkaz: https://doaj.org/article/7fdfb43a419b4281bc5d86b2cd8ea8f8

The inner structure of boundary quotients of right LCM semigroups

Autor: Nicolai Stammeier, Stefano Rossi, Roberto Conti, Valeriano Aiello

Publikováno v: Aiello, Valeriano; Conti, Roberto; Rossi, Stefano; Stammeier, Nicolai (2020). The inner structure of boundary quotients of right LCM semigroups. Indiana University mathematics journal, 69(5), pp. 1627-1661. Dept. of Mathematics, Indiana University 10.1512/iumj.2020.69.8006

We study distinguished subalgebras and automorphisms of boundary quotients arising from algebraic dynamical systems $(G,P,\theta)$. Our work includes a complete solution to the problem of extending Bogolubov automorphisms from the Cuntz algebra in $2

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef56300cb0e3e639c10e6ec224390e1d
https://doi.org/10.1512/iumj.2020.69.8006

On the cyclic automorphism of the Cuntz algebra and its fixed-point algebra

Autor: Valeriano Aiello, Stefano Rossi

We investigate the structure of the fixed-point algebra of $\mathcal{O}_n$ under the action of the cyclic permutation of the generating isometries. We prove that it is $*$-isomorphic with $\mathcal{O}_n$, thus generalizing a result of Choi and Latr\'

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c622cc1da36e86e219b9812a05e30693
http://arxiv.org/abs/2107.02154

The Homflypt polynomial and the oriented Thompson group

Autor: Vaughan F. R. Jones, Valeriano Aiello, Roberto Conti

Publikováno v: Quantum Topology. 9:461-472

We show how to construct unitary representations of the oriented Thompson group $\vec{F}$ from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of $\vec{F}$.
Co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::198848059911b2f7d4fea0472a1fbf7d
https://doi.org/10.4171/qt/112

Diagonal automorphisms of the 2-adic ring C*-algebra

Autor: Stefano Rossi, Valeriano Aiello, Roberto Conti

Publikováno v: The Quarterly Journal of Mathematics

The $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$ naturally contains a copy of the Cuntz algebra $\mathcal{O}_2$ and, a fortiori, also of its diagonal subalgebra $\mathcal{D}_2$ with Cantor spectrum. This paper is aimed at studying the group ${\rm Aut}

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29c58c544b719f69c24a2ebb6a86d51f
https://doi.org/10.1093/qmath/hax064